Vol. 7, No. 05
from Professor Cleary
Marsha Mallow and Maura Thesame have forgotten one little thing about capability analysis: it is generally assumed that the data represents a normal distribution. A visual review of the data indicates that it does not follow this pattern at all:
Using CHARTrunner, Jack D. Ripper performs a Chi-squared test and concludes that the Dynamic Duo’s assumption of normalcy is invalid. [Note, To review Chi-squared tests, click HERE for a previous video relating to this concept.]
Although it appears that the two managers have created quite a muddle with their analysis of the data, it is possible to pursue capability analysis with the existing data by using CHARTrunner, using the non-normal feature in the software.
Pearson curve fitting is a method of analyzing data against predetermined shapes for distributions. The procedure estimates what is referred to as the “k factor” from the data, then selects the type of curve (distribution). The data is then analyzed using this distribution. A Chi-squared test is performed to see if the data is in agreement with the curve selected (pass), or significantly different (rejected).
In this case, CHARTrunner has selected the beta distribution:
As the chart indicates, this distribution fits the data better than the normal. This is reflected in the Chi-squared value going down to 3.75 and the software’s determination that the data truly follows the beta with a confidence of 95 percent. Also notable is the fact that the Cpk went from .78 to 1.03. If only Marty had known about CHARTrunner, he might have been able to save his job…
The Dynamic Duo may be facing a Rocky Road unless they learn a little more about this statistical concept.
Copyright 2005 PQ Systems.
Please direct questions or problems regarding this web site to the Webmaster.